Simultaneous Capacity and Production Management of Short-Life-Cycle, Produce-to-Stock Goods Under Stochastic Demand

This paper derives the optimal simultaneous capacity and production plan for a shortlife-cycle, produce-to-stock good under stochastic demand. Capacity can be reduced as well as added, at exogenously set unit prices. In both cases studied, with and without carryover of unsold units, a target interval policy is optimal: There is a (usually different) target interval for each period such that capacity should be changed as little as possible to bring the level available into that interval. Our contribution in the case of no carry-over, is a detailed characterization of the target intervals, assuming demands increase stochastically at the beginning of the life cycle and decrease thereafter. In the case of carry-over, we establish the general result and show that capacity and inventory are economic substitutes: The target intervals decrease in the initial stock level and the optimal unconstrained base stock level decreases in the capacity level. In both cases, optimal service rates are not necessarily constant over time. A numerical example illustrates the results.

[1]  Arnoldo C. Hax,et al.  Production and inventory management , 1983 .

[2]  S. Sethi,et al.  Planning for surprise: water resources development under demand and supply uncertainty. I. the general model , 1989 .

[3]  Richard V. Evans.  Inventory control of a multiproduct system with a limited production resource , 1967 .

[4]  Shanling Li,et al.  Dynamic Capacity Expansion Problem with Multiple Products: Technology Selection and Timing of Capacity Additions , 1994, Oper. Res..

[5]  Janice C. Eberly,et al.  Multi-Factor Dynamic Investment Under Uncertainty , 1996 .

[6]  Awi Federgruen,et al.  Stochastic Inventory Models with Limited Production Capacity and Periodically Varying Parameters , 1997, Probability in the Engineering and Informational Sciences.

[7]  D. M. Topkis.  Supermodularity and Complementarity , 1998 .

[8]  J. Michael Harrison,et al.  Multi-Resource Investment Strategies: Operational Hedging Under Demand Uncertainty , 1997, Eur. J. Oper. Res..

[9]  Sridhar R. Tayur,et al.  A Capacitated Production-Inventory Model with Periodic Demand , 1998, Oper. Res..

[10]  John A. Buzacott,et al.  Capacity expansion with interrupted demand growth , 1988 .

[11]  Donald M. Topkis,et al.  Minimizing a Submodular Function on a Lattice , 1978, Oper. Res..

[12]  M. R. Rao,et al.  Optimal Capacity Expansion with Inventory , 1976, Oper. Res..

[13]  Izak Duenyas,et al.  A Stopping Rule for Forecasting Horizons in Nonhomogeneous Markov Decision Processes , 1992, Oper. Res..

[14]  W. Karush.  A theorem in convex programming , 1959 .

[15]  S. C. Wood,et al.  Optimal Sizing and Timing of Modular Capacity Expansions , 2000 .

[16]  Hanan Luss,et al.  Operations Research and Capacity Expansion Problems: A Survey , 1982, Oper. Res..

[17]  Andreas C. Soteriou,et al.  Capacity acquisition and disposal with discrete facility sizes , 1994 .

[18]  Awi Federgruen,et al.  An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion , 1986, Math. Oper. Res..

[19]  Christoph A. Schneeweiß.  The General Model , 1977 .

[20]  J. V. Mieghem.  Investment Strategies for Flexible Resources , 1998 .

[21]  Daniel P. Heyman,et al.  Stochastic models in operations research , 1982 .

[22]  J. C. Bean,et al.  Optimal Capacity Expansion Over an Infinite Horizon , 1985 .

[23]  Robert L. Smith,et al.  Capacity Expansion Under Stochastic Demands , 1992, Oper. Res..

[24]  George W. Evans,et al.  A transportation and production model , 1958 .

[25]  G. C. Varvaloucas,et al.  Capacity Expansion/Contraction of a Facility with Demand Augmentation Dynamics , 1984, Oper. Res..

[26]  A. S. Manne.  CAPACITY EXPANSION AND PROBABILISTIC GROWTH , 1961 .

[27]  T. Morton,et al.  Capacity Expansion and Replacement in Growing Markets with Uncertain Technological Breakthroughs , 1998 .